Summary
In the present note we provide a complete characterization of all Runge-Kutta methods which generate a canonical transformation if applied to a Hamiltonian system of ordinary differential equations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. I. Arnold (Ed.), Dynamical Systems III. Encyclopedia of Mathematical Sciences Vol. 3. Springer-Verlag, Berlin, Heidelberg, 1988.
Feng Kang, Difference schemes for Hamiltonian formalism and sympiectic geometry. J. of Comp. Math.,4, 279–289 (1986).
E. Hairer, Algebraically stable and implementable Runge-Kutta methods of high-order. SIAM J. Numer. Anal.,18, No. 6, 1981.
E. Hairer, S. P. Norsett, G. Wanner, Solving ordinary differential equations I. Springer Series in Computational Math.,8, 1987.
F. C. Iselin, Algorithms for Tracking Charged Particles in Circular Accelerators. Lect. Notes in Physics, 247, Springer, Berlin, 1986.
D. M. Stoffer, Some geometric and numerical methods for perturbed integrated systems. Diss. ETH, No. 8456, Zürich, 1988.
F. M. Lasagni, in preparation, to appear in Numerische Mathematik.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lasagni, F.M. Canonical Runge-Kutta methods. Z. angew. Math. Phys. 39, 952–953 (1988). https://doi.org/10.1007/BF00945133
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00945133